Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(148.845356651\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −24.0067 | −1.06095 | −0.530477 | − | 0.847699i | \(-0.677987\pi\) | ||||
−0.530477 | + | 0.847699i | \(0.677987\pi\) | |||||||
\(3\) | −194.286 | −1.38483 | −0.692413 | − | 0.721502i | \(-0.743452\pi\) | ||||
−0.692413 | + | 0.721502i | \(0.743452\pi\) | |||||||
\(4\) | 64.3195 | 0.125624 | ||||||||
\(5\) | 2543.89 | 1.82026 | 0.910129 | − | 0.414326i | \(-0.135982\pi\) | ||||
0.910129 | + | 0.414326i | \(0.135982\pi\) | |||||||
\(6\) | 4664.15 | 1.46924 | ||||||||
\(7\) | −1962.84 | −0.308990 | −0.154495 | − | 0.987994i | \(-0.549375\pi\) | ||||
−0.154495 | + | 0.987994i | \(0.549375\pi\) | |||||||
\(8\) | 10747.3 | 0.927673 | ||||||||
\(9\) | 18063.9 | 0.917740 | ||||||||
\(10\) | −61070.2 | −1.93121 | ||||||||
\(11\) | 18226.6 | 0.375352 | 0.187676 | − | 0.982231i | \(-0.439905\pi\) | ||||
0.187676 | + | 0.982231i | \(0.439905\pi\) | |||||||
\(12\) | −12496.4 | −0.173967 | ||||||||
\(13\) | −165432. | −1.60648 | −0.803240 | − | 0.595656i | \(-0.796892\pi\) | ||||
−0.803240 | + | 0.595656i | \(0.796892\pi\) | |||||||
\(14\) | 47121.2 | 0.327824 | ||||||||
\(15\) | −494241. | −2.52074 | ||||||||
\(16\) | −290939. | −1.10984 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −433653. | −0.973681 | ||||||||
\(19\) | 137579. | 0.242193 | 0.121097 | − | 0.992641i | \(-0.461359\pi\) | ||||
0.121097 | + | 0.992641i | \(0.461359\pi\) | |||||||
\(20\) | 163622. | 0.228668 | ||||||||
\(21\) | 381352. | 0.427897 | ||||||||
\(22\) | −437559. | −0.398231 | ||||||||
\(23\) | 695539. | 0.518258 | 0.259129 | − | 0.965843i | \(-0.416565\pi\) | ||||
0.259129 | + | 0.965843i | \(0.416565\pi\) | |||||||
\(24\) | −2.08805e6 | −1.28466 | ||||||||
\(25\) | 4.51824e6 | 2.31334 | ||||||||
\(26\) | 3.97148e6 | 1.70440 | ||||||||
\(27\) | 314571. | 0.113915 | ||||||||
\(28\) | −126249. | −0.0388165 | ||||||||
\(29\) | 4.23015e6 | 1.11062 | 0.555309 | − | 0.831644i | \(-0.312600\pi\) | ||||
0.555309 | + | 0.831644i | \(0.312600\pi\) | |||||||
\(30\) | 1.18651e7 | 2.67439 | ||||||||
\(31\) | 3.78840e6 | 0.736764 | 0.368382 | − | 0.929675i | \(-0.379912\pi\) | ||||
0.368382 | + | 0.929675i | \(0.379912\pi\) | |||||||
\(32\) | 1.48184e6 | 0.249819 | ||||||||
\(33\) | −3.54116e6 | −0.519796 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.99325e6 | −0.562441 | ||||||||
\(36\) | 1.16186e6 | 0.115290 | ||||||||
\(37\) | −1.18678e7 | −1.04103 | −0.520513 | − | 0.853854i | \(-0.674259\pi\) | ||||
−0.520513 | + | 0.853854i | \(0.674259\pi\) | |||||||
\(38\) | −3.30282e6 | −0.256956 | ||||||||
\(39\) | 3.21411e7 | 2.22469 | ||||||||
\(40\) | 2.73399e7 | 1.68860 | ||||||||
\(41\) | 9.83530e6 | 0.543576 | 0.271788 | − | 0.962357i | \(-0.412385\pi\) | ||||
0.271788 | + | 0.962357i | \(0.412385\pi\) | |||||||
\(42\) | −9.15498e6 | −0.453979 | ||||||||
\(43\) | −3.54345e7 | −1.58059 | −0.790293 | − | 0.612729i | \(-0.790072\pi\) | ||||
−0.790293 | + | 0.612729i | \(0.790072\pi\) | |||||||
\(44\) | 1.17233e6 | 0.0471532 | ||||||||
\(45\) | 4.59525e7 | 1.67052 | ||||||||
\(46\) | −1.66976e7 | −0.549848 | ||||||||
\(47\) | 5.08554e7 | 1.52018 | 0.760092 | − | 0.649815i | \(-0.225154\pi\) | ||||
0.760092 | + | 0.649815i | \(0.225154\pi\) | |||||||
\(48\) | 5.65252e7 | 1.53694 | ||||||||
\(49\) | −3.65009e7 | −0.904525 | ||||||||
\(50\) | −1.08468e8 | −2.45435 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.06405e7 | −0.201813 | ||||||||
\(53\) | 1.55202e7 | 0.270182 | 0.135091 | − | 0.990833i | \(-0.456867\pi\) | ||||
0.135091 | + | 0.990833i | \(0.456867\pi\) | |||||||
\(54\) | −7.55180e6 | −0.120859 | ||||||||
\(55\) | 4.63664e7 | 0.683237 | ||||||||
\(56\) | −2.10953e7 | −0.286641 | ||||||||
\(57\) | −2.67297e7 | −0.335395 | ||||||||
\(58\) | −1.01552e8 | −1.17831 | ||||||||
\(59\) | −9.29686e7 | −0.998854 | −0.499427 | − | 0.866356i | \(-0.666456\pi\) | ||||
−0.499427 | + | 0.866356i | \(0.666456\pi\) | |||||||
\(60\) | −3.17893e7 | −0.316665 | ||||||||
\(61\) | 2.04285e8 | 1.88909 | 0.944543 | − | 0.328387i | \(-0.106505\pi\) | ||||
0.944543 | + | 0.328387i | \(0.106505\pi\) | |||||||
\(62\) | −9.09468e7 | −0.781673 | ||||||||
\(63\) | −3.54565e7 | −0.283572 | ||||||||
\(64\) | 1.13387e8 | 0.844796 | ||||||||
\(65\) | −4.20841e8 | −2.92421 | ||||||||
\(66\) | 8.50115e7 | 0.551480 | ||||||||
\(67\) | 5.35413e7 | 0.324603 | 0.162301 | − | 0.986741i | \(-0.448108\pi\) | ||||
0.162301 | + | 0.986741i | \(0.448108\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.35133e8 | −0.717697 | ||||||||
\(70\) | 1.19871e8 | 0.596724 | ||||||||
\(71\) | 1.33664e8 | 0.624242 | 0.312121 | − | 0.950042i | \(-0.398961\pi\) | ||||
0.312121 | + | 0.950042i | \(0.398961\pi\) | |||||||
\(72\) | 1.94138e8 | 0.851363 | ||||||||
\(73\) | −4.37702e7 | −0.180395 | −0.0901977 | − | 0.995924i | \(-0.528750\pi\) | ||||
−0.0901977 | + | 0.995924i | \(0.528750\pi\) | |||||||
\(74\) | 2.84906e8 | 1.10448 | ||||||||
\(75\) | −8.77828e8 | −3.20357 | ||||||||
\(76\) | 8.84904e6 | 0.0304253 | ||||||||
\(77\) | −3.57759e7 | −0.115980 | ||||||||
\(78\) | −7.71600e8 | −2.36030 | ||||||||
\(79\) | −1.37020e8 | −0.395787 | −0.197893 | − | 0.980224i | \(-0.563410\pi\) | ||||
−0.197893 | + | 0.980224i | \(0.563410\pi\) | |||||||
\(80\) | −7.40115e8 | −2.02020 | ||||||||
\(81\) | −4.16668e8 | −1.07549 | ||||||||
\(82\) | −2.36113e8 | −0.576709 | ||||||||
\(83\) | −4.10757e8 | −0.950023 | −0.475011 | − | 0.879980i | \(-0.657556\pi\) | ||||
−0.475011 | + | 0.879980i | \(0.657556\pi\) | |||||||
\(84\) | 2.45284e7 | 0.0537541 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.50664e8 | 1.67693 | ||||||||
\(87\) | −8.21856e8 | −1.53801 | ||||||||
\(88\) | 1.95887e8 | 0.348204 | ||||||||
\(89\) | 2.89162e8 | 0.488524 | 0.244262 | − | 0.969709i | \(-0.421454\pi\) | ||||
0.244262 | + | 0.969709i | \(0.421454\pi\) | |||||||
\(90\) | −1.10317e9 | −1.77235 | ||||||||
\(91\) | 3.24717e8 | 0.496385 | ||||||||
\(92\) | 4.47367e7 | 0.0651057 | ||||||||
\(93\) | −7.36032e8 | −1.02029 | ||||||||
\(94\) | −1.22087e9 | −1.61285 | ||||||||
\(95\) | 3.49986e8 | 0.440854 | ||||||||
\(96\) | −2.87900e8 | −0.345956 | ||||||||
\(97\) | 2.82905e8 | 0.324465 | 0.162233 | − | 0.986753i | \(-0.448131\pi\) | ||||
0.162233 | + | 0.986753i | \(0.448131\pi\) | |||||||
\(98\) | 8.76264e8 | 0.959660 | ||||||||
\(99\) | 3.29243e8 | 0.344475 | ||||||||
\(100\) | 2.90611e8 | 0.290611 | ||||||||
\(101\) | 2.20849e8 | 0.211179 | 0.105589 | − | 0.994410i | \(-0.466327\pi\) | ||||
0.105589 | + | 0.994410i | \(0.466327\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.05360e8 | −0.0922372 | −0.0461186 | − | 0.998936i | \(-0.514685\pi\) | ||||
−0.0461186 | + | 0.998936i | \(0.514685\pi\) | |||||||
\(104\) | −1.77795e9 | −1.49029 | ||||||||
\(105\) | 9.70116e8 | 0.778882 | ||||||||
\(106\) | −3.72588e8 | −0.286651 | ||||||||
\(107\) | −4.96752e8 | −0.366364 | −0.183182 | − | 0.983079i | \(-0.558640\pi\) | ||||
−0.183182 | + | 0.983079i | \(0.558640\pi\) | |||||||
\(108\) | 2.02331e7 | 0.0143105 | ||||||||
\(109\) | −6.36599e8 | −0.431963 | −0.215982 | − | 0.976397i | \(-0.569295\pi\) | ||||
−0.215982 | + | 0.976397i | \(0.569295\pi\) | |||||||
\(110\) | −1.11310e9 | −0.724883 | ||||||||
\(111\) | 2.30574e9 | 1.44164 | ||||||||
\(112\) | 5.71066e8 | 0.342930 | ||||||||
\(113\) | −9.53685e8 | −0.550240 | −0.275120 | − | 0.961410i | \(-0.588718\pi\) | ||||
−0.275120 | + | 0.961410i | \(0.588718\pi\) | |||||||
\(114\) | 6.41690e8 | 0.355839 | ||||||||
\(115\) | 1.76937e9 | 0.943363 | ||||||||
\(116\) | 2.72081e8 | 0.139520 | ||||||||
\(117\) | −2.98835e9 | −1.47433 | ||||||||
\(118\) | 2.23186e9 | 1.05974 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −5.31176e9 | −2.33842 | ||||||||
\(121\) | −2.02574e9 | −0.859111 | ||||||||
\(122\) | −4.90419e9 | −2.00423 | ||||||||
\(123\) | −1.91086e9 | −0.752757 | ||||||||
\(124\) | 2.43668e8 | 0.0925553 | ||||||||
\(125\) | 6.52536e9 | 2.39061 | ||||||||
\(126\) | 8.51193e8 | 0.300857 | ||||||||
\(127\) | 5.40081e9 | 1.84222 | 0.921111 | − | 0.389299i | \(-0.127283\pi\) | ||||
0.921111 | + | 0.389299i | \(0.127283\pi\) | |||||||
\(128\) | −3.48073e9 | −1.14611 | ||||||||
\(129\) | 6.88441e9 | 2.18884 | ||||||||
\(130\) | 1.01030e10 | 3.10245 | ||||||||
\(131\) | −2.76594e9 | −0.820582 | −0.410291 | − | 0.911955i | \(-0.634573\pi\) | ||||
−0.410291 | + | 0.911955i | \(0.634573\pi\) | |||||||
\(132\) | −2.27766e8 | −0.0652989 | ||||||||
\(133\) | −2.70046e8 | −0.0748352 | ||||||||
\(134\) | −1.28535e9 | −0.344389 | ||||||||
\(135\) | 8.00233e8 | 0.207355 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.06041e9 | −0.742228 | −0.371114 | − | 0.928587i | \(-0.621024\pi\) | ||||
−0.371114 | + | 0.928587i | \(0.621024\pi\) | |||||||
\(138\) | 3.24409e9 | 0.761443 | ||||||||
\(139\) | 3.55042e9 | 0.806702 | 0.403351 | − | 0.915045i | \(-0.367845\pi\) | ||||
0.403351 | + | 0.915045i | \(0.367845\pi\) | |||||||
\(140\) | −3.21163e8 | −0.0706561 | ||||||||
\(141\) | −9.88046e9 | −2.10519 | ||||||||
\(142\) | −3.20883e9 | −0.662292 | ||||||||
\(143\) | −3.01527e9 | −0.602995 | ||||||||
\(144\) | −5.25548e9 | −1.01855 | ||||||||
\(145\) | 1.07610e10 | 2.02161 | ||||||||
\(146\) | 1.05078e9 | 0.191391 | ||||||||
\(147\) | 7.09159e9 | 1.25261 | ||||||||
\(148\) | −7.63330e8 | −0.130778 | ||||||||
\(149\) | −3.88137e9 | −0.645130 | −0.322565 | − | 0.946547i | \(-0.604545\pi\) | ||||
−0.322565 | + | 0.946547i | \(0.604545\pi\) | |||||||
\(150\) | 2.10737e10 | 3.39884 | ||||||||
\(151\) | 8.28467e9 | 1.29682 | 0.648409 | − | 0.761292i | \(-0.275435\pi\) | ||||
0.648409 | + | 0.761292i | \(0.275435\pi\) | |||||||
\(152\) | 1.47861e9 | 0.224676 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.58860e8 | 0.123049 | ||||||||
\(155\) | 9.63727e9 | 1.34110 | ||||||||
\(156\) | 2.06730e9 | 0.279475 | ||||||||
\(157\) | −1.15724e10 | −1.52011 | −0.760053 | − | 0.649861i | \(-0.774827\pi\) | ||||
−0.760053 | + | 0.649861i | \(0.774827\pi\) | |||||||
\(158\) | 3.28939e9 | 0.419912 | ||||||||
\(159\) | −3.01535e9 | −0.374155 | ||||||||
\(160\) | 3.76963e9 | 0.454736 | ||||||||
\(161\) | −1.36523e9 | −0.160136 | ||||||||
\(162\) | 1.00028e10 | 1.14105 | ||||||||
\(163\) | 7.06563e9 | 0.783983 | 0.391991 | − | 0.919969i | \(-0.371786\pi\) | ||||
0.391991 | + | 0.919969i | \(0.371786\pi\) | |||||||
\(164\) | 6.32602e8 | 0.0682862 | ||||||||
\(165\) | −9.00832e9 | −0.946163 | ||||||||
\(166\) | 9.86091e9 | 1.00793 | ||||||||
\(167\) | −9.51502e9 | −0.946642 | −0.473321 | − | 0.880890i | \(-0.656945\pi\) | ||||
−0.473321 | + | 0.880890i | \(0.656945\pi\) | |||||||
\(168\) | 4.09850e9 | 0.396948 | ||||||||
\(169\) | 1.67633e10 | 1.58078 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.48522e9 | 0.222270 | ||||||||
\(172\) | −2.27913e9 | −0.198560 | ||||||||
\(173\) | −1.34873e10 | −1.14477 | −0.572385 | − | 0.819985i | \(-0.693982\pi\) | ||||
−0.572385 | + | 0.819985i | \(0.693982\pi\) | |||||||
\(174\) | 1.97300e10 | 1.63176 | ||||||||
\(175\) | −8.86858e9 | −0.714797 | ||||||||
\(176\) | −5.30282e9 | −0.416581 | ||||||||
\(177\) | 1.80625e10 | 1.38324 | ||||||||
\(178\) | −6.94181e9 | −0.518302 | ||||||||
\(179\) | −2.32156e10 | −1.69021 | −0.845107 | − | 0.534597i | \(-0.820463\pi\) | ||||
−0.845107 | + | 0.534597i | \(0.820463\pi\) | |||||||
\(180\) | 2.95564e9 | 0.209858 | ||||||||
\(181\) | −1.04604e10 | −0.724425 | −0.362212 | − | 0.932096i | \(-0.617978\pi\) | ||||
−0.362212 | + | 0.932096i | \(0.617978\pi\) | |||||||
\(182\) | −7.79537e9 | −0.526642 | ||||||||
\(183\) | −3.96896e10 | −2.61605 | ||||||||
\(184\) | 7.47517e9 | 0.480774 | ||||||||
\(185\) | −3.01903e10 | −1.89493 | ||||||||
\(186\) | 1.76697e10 | 1.08248 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.27099e9 | 0.190972 | ||||||||
\(189\) | −6.17453e8 | −0.0351986 | ||||||||
\(190\) | −8.40200e9 | −0.467726 | ||||||||
\(191\) | 2.86896e10 | 1.55982 | 0.779909 | − | 0.625893i | \(-0.215265\pi\) | ||||
0.779909 | + | 0.625893i | \(0.215265\pi\) | |||||||
\(192\) | −2.20294e10 | −1.16989 | ||||||||
\(193\) | −1.05634e9 | −0.0548022 | −0.0274011 | − | 0.999625i | \(-0.508723\pi\) | ||||
−0.0274011 | + | 0.999625i | \(0.508723\pi\) | |||||||
\(194\) | −6.79161e9 | −0.344243 | ||||||||
\(195\) | 8.17633e10 | 4.04951 | ||||||||
\(196\) | −2.34772e9 | −0.113630 | ||||||||
\(197\) | 1.48923e9 | 0.0704474 | 0.0352237 | − | 0.999379i | \(-0.488786\pi\) | ||||
0.0352237 | + | 0.999379i | \(0.488786\pi\) | |||||||
\(198\) | −7.90402e9 | −0.365473 | ||||||||
\(199\) | −1.25548e10 | −0.567504 | −0.283752 | − | 0.958898i | \(-0.591579\pi\) | ||||
−0.283752 | + | 0.958898i | \(0.591579\pi\) | |||||||
\(200\) | 4.85589e10 | 2.14602 | ||||||||
\(201\) | −1.04023e10 | −0.449518 | ||||||||
\(202\) | −5.30186e9 | −0.224051 | ||||||||
\(203\) | −8.30310e9 | −0.343169 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.50199e10 | 0.989448 | ||||||||
\(206\) | 2.52933e9 | 0.0978595 | ||||||||
\(207\) | 1.25641e10 | 0.475626 | ||||||||
\(208\) | 4.81306e10 | 1.78294 | ||||||||
\(209\) | 2.50760e9 | 0.0909076 | ||||||||
\(210\) | −2.32892e10 | −0.826358 | ||||||||
\(211\) | 3.03540e10 | 1.05425 | 0.527127 | − | 0.849787i | \(-0.323269\pi\) | ||||
0.527127 | + | 0.849787i | \(0.323269\pi\) | |||||||
\(212\) | 9.98253e8 | 0.0339414 | ||||||||
\(213\) | −2.59691e10 | −0.864466 | ||||||||
\(214\) | 1.19253e10 | 0.388695 | ||||||||
\(215\) | −9.01413e10 | −2.87707 | ||||||||
\(216\) | 3.38079e9 | 0.105676 | ||||||||
\(217\) | −7.43603e9 | −0.227652 | ||||||||
\(218\) | 1.52826e10 | 0.458293 | ||||||||
\(219\) | 8.50392e9 | 0.249816 | ||||||||
\(220\) | 2.98226e9 | 0.0858310 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5.53530e10 | −1.52951 | ||||||||
\(223\) | 2.73787e10 | 0.741380 | 0.370690 | − | 0.928757i | \(-0.379121\pi\) | ||||
0.370690 | + | 0.928757i | \(0.379121\pi\) | |||||||
\(224\) | −2.90862e9 | −0.0771916 | ||||||||
\(225\) | 8.16169e10 | 2.12304 | ||||||||
\(226\) | 2.28948e10 | 0.583779 | ||||||||
\(227\) | −3.41868e10 | −0.854560 | −0.427280 | − | 0.904119i | \(-0.640528\pi\) | ||||
−0.427280 | + | 0.904119i | \(0.640528\pi\) | |||||||
\(228\) | −1.71924e9 | −0.0421337 | ||||||||
\(229\) | 3.42397e9 | 0.0822753 | 0.0411377 | − | 0.999153i | \(-0.486902\pi\) | ||||
0.0411377 | + | 0.999153i | \(0.486902\pi\) | |||||||
\(230\) | −4.24767e10 | −1.00087 | ||||||||
\(231\) | 6.95074e9 | 0.160612 | ||||||||
\(232\) | 4.54627e10 | 1.03029 | ||||||||
\(233\) | −3.46809e10 | −0.770882 | −0.385441 | − | 0.922732i | \(-0.625951\pi\) | ||||
−0.385441 | + | 0.922732i | \(0.625951\pi\) | |||||||
\(234\) | 7.17403e10 | 1.56420 | ||||||||
\(235\) | 1.29370e11 | 2.76713 | ||||||||
\(236\) | −5.97970e9 | −0.125480 | ||||||||
\(237\) | 2.66210e10 | 0.548096 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.84083e10 | 1.35618 | 0.678092 | − | 0.734977i | \(-0.262807\pi\) | ||||
0.678092 | + | 0.734977i | \(0.262807\pi\) | |||||||
\(240\) | 1.43794e11 | 2.79762 | ||||||||
\(241\) | 2.87585e10 | 0.549148 | 0.274574 | − | 0.961566i | \(-0.411463\pi\) | ||||
0.274574 | + | 0.961566i | \(0.411463\pi\) | |||||||
\(242\) | 4.86312e10 | 0.911478 | ||||||||
\(243\) | 7.47609e10 | 1.37545 | ||||||||
\(244\) | 1.31395e10 | 0.237315 | ||||||||
\(245\) | −9.28541e10 | −1.64647 | ||||||||
\(246\) | 4.58733e10 | 0.798641 | ||||||||
\(247\) | −2.27601e10 | −0.389078 | ||||||||
\(248\) | 4.07151e10 | 0.683476 | ||||||||
\(249\) | 7.98042e10 | 1.31562 | ||||||||
\(250\) | −1.56652e11 | −2.53633 | ||||||||
\(251\) | 5.08079e10 | 0.807978 | 0.403989 | − | 0.914764i | \(-0.367623\pi\) | ||||
0.403989 | + | 0.914764i | \(0.367623\pi\) | |||||||
\(252\) | −2.28055e9 | −0.0356235 | ||||||||
\(253\) | 1.26773e10 | 0.194529 | ||||||||
\(254\) | −1.29655e11 | −1.95451 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.55069e10 | 0.371174 | ||||||||
\(257\) | 4.43960e10 | 0.634811 | 0.317406 | − | 0.948290i | \(-0.397188\pi\) | ||||
0.317406 | + | 0.948290i | \(0.397188\pi\) | |||||||
\(258\) | −1.65272e11 | −2.32225 | ||||||||
\(259\) | 2.32945e10 | 0.321666 | ||||||||
\(260\) | −2.70683e10 | −0.367351 | ||||||||
\(261\) | 7.64129e10 | 1.01926 | ||||||||
\(262\) | 6.64010e10 | 0.870600 | ||||||||
\(263\) | 4.45406e10 | 0.574057 | 0.287028 | − | 0.957922i | \(-0.407333\pi\) | ||||
0.287028 | + | 0.957922i | \(0.407333\pi\) | |||||||
\(264\) | −3.80580e10 | −0.482201 | ||||||||
\(265\) | 3.94817e10 | 0.491801 | ||||||||
\(266\) | 6.48291e9 | 0.0793967 | ||||||||
\(267\) | −5.61800e10 | −0.676520 | ||||||||
\(268\) | 3.44375e9 | 0.0407779 | ||||||||
\(269\) | −7.75647e10 | −0.903189 | −0.451594 | − | 0.892223i | \(-0.649145\pi\) | ||||
−0.451594 | + | 0.892223i | \(0.649145\pi\) | |||||||
\(270\) | −1.92109e10 | −0.219994 | ||||||||
\(271\) | 2.04736e10 | 0.230586 | 0.115293 | − | 0.993332i | \(-0.463219\pi\) | ||||
0.115293 | + | 0.993332i | \(0.463219\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.30879e10 | −0.687407 | ||||||||
\(274\) | 7.34703e10 | 0.787470 | ||||||||
\(275\) | 8.23521e10 | 0.868315 | ||||||||
\(276\) | −8.69170e9 | −0.0901600 | ||||||||
\(277\) | −9.13323e10 | −0.932106 | −0.466053 | − | 0.884757i | \(-0.654324\pi\) | ||||
−0.466053 | + | 0.884757i | \(0.654324\pi\) | |||||||
\(278\) | −8.52337e10 | −0.855874 | ||||||||
\(279\) | 6.84332e10 | 0.676158 | ||||||||
\(280\) | −5.36640e10 | −0.521761 | ||||||||
\(281\) | 1.59049e11 | 1.52179 | 0.760893 | − | 0.648877i | \(-0.224761\pi\) | ||||
0.760893 | + | 0.648877i | \(0.224761\pi\) | |||||||
\(282\) | 2.37197e11 | 2.23351 | ||||||||
\(283\) | −4.93813e10 | −0.457639 | −0.228820 | − | 0.973469i | \(-0.573487\pi\) | ||||
−0.228820 | + | 0.973469i | \(0.573487\pi\) | |||||||
\(284\) | 8.59723e9 | 0.0784198 | ||||||||
\(285\) | −6.79973e10 | −0.610506 | ||||||||
\(286\) | 7.23865e10 | 0.639750 | ||||||||
\(287\) | −1.93051e10 | −0.167959 | ||||||||
\(288\) | 2.67678e10 | 0.229269 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −2.58336e11 | −2.14484 | ||||||||
\(291\) | −5.49644e10 | −0.449328 | ||||||||
\(292\) | −2.81528e9 | −0.0226620 | ||||||||
\(293\) | 9.46411e10 | 0.750197 | 0.375099 | − | 0.926985i | \(-0.377609\pi\) | ||||
0.375099 | + | 0.926985i | \(0.377609\pi\) | |||||||
\(294\) | −1.70245e11 | −1.32896 | ||||||||
\(295\) | −2.36502e11 | −1.81817 | ||||||||
\(296\) | −1.27547e11 | −0.965731 | ||||||||
\(297\) | 5.73356e9 | 0.0427583 | ||||||||
\(298\) | 9.31787e10 | 0.684453 | ||||||||
\(299\) | −1.15065e11 | −0.832571 | ||||||||
\(300\) | −5.64615e10 | −0.402445 | ||||||||
\(301\) | 6.95523e10 | 0.488385 | ||||||||
\(302\) | −1.98887e11 | −1.37586 | ||||||||
\(303\) | −4.29079e10 | −0.292446 | ||||||||
\(304\) | −4.00271e10 | −0.268796 | ||||||||
\(305\) | 5.19677e11 | 3.43862 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.91043e11 | 1.22746 | 0.613731 | − | 0.789515i | \(-0.289668\pi\) | ||||
0.613731 | + | 0.789515i | \(0.289668\pi\) | |||||||
\(308\) | −2.30109e9 | −0.0145699 | ||||||||
\(309\) | 2.04698e10 | 0.127732 | ||||||||
\(310\) | −2.31359e11 | −1.42285 | ||||||||
\(311\) | −1.82343e11 | −1.10526 | −0.552632 | − | 0.833425i | \(-0.686377\pi\) | ||||
−0.552632 | + | 0.833425i | \(0.686377\pi\) | |||||||
\(312\) | 3.45430e11 | 2.06379 | ||||||||
\(313\) | 2.16835e11 | 1.27697 | 0.638483 | − | 0.769636i | \(-0.279562\pi\) | ||||
0.638483 | + | 0.769636i | \(0.279562\pi\) | |||||||
\(314\) | 2.77814e11 | 1.61276 | ||||||||
\(315\) | −9.01974e10 | −0.516174 | ||||||||
\(316\) | −8.81305e9 | −0.0497204 | ||||||||
\(317\) | 2.39301e11 | 1.33100 | 0.665499 | − | 0.746399i | \(-0.268219\pi\) | ||||
0.665499 | + | 0.746399i | \(0.268219\pi\) | |||||||
\(318\) | 7.23885e10 | 0.396961 | ||||||||
\(319\) | 7.71011e10 | 0.416872 | ||||||||
\(320\) | 2.88443e11 | 1.53775 | ||||||||
\(321\) | 9.65117e10 | 0.507350 | ||||||||
\(322\) | 3.27747e10 | 0.169897 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.67999e10 | −0.135108 | ||||||||
\(325\) | −7.47462e11 | −3.71633 | ||||||||
\(326\) | −1.69622e11 | −0.831770 | ||||||||
\(327\) | 1.23682e11 | 0.598194 | ||||||||
\(328\) | 1.05703e11 | 0.504260 | ||||||||
\(329\) | −9.98210e10 | −0.469721 | ||||||||
\(330\) | 2.16260e11 | 1.00384 | ||||||||
\(331\) | −2.69499e11 | −1.23404 | −0.617022 | − | 0.786946i | \(-0.711661\pi\) | ||||
−0.617022 | + | 0.786946i | \(0.711661\pi\) | |||||||
\(332\) | −2.64197e10 | −0.119346 | ||||||||
\(333\) | −2.14378e11 | −0.955391 | ||||||||
\(334\) | 2.28424e11 | 1.00434 | ||||||||
\(335\) | 1.36203e11 | 0.590860 | ||||||||
\(336\) | −1.10950e11 | −0.474898 | ||||||||
\(337\) | 1.88865e11 | 0.797657 | 0.398828 | − | 0.917026i | \(-0.369417\pi\) | ||||
0.398828 | + | 0.917026i | \(0.369417\pi\) | |||||||
\(338\) | −4.02432e11 | −1.67713 | ||||||||
\(339\) | 1.85287e11 | 0.761985 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.90496e10 | 0.276546 | ||||||||
\(342\) | −5.96617e10 | −0.235819 | ||||||||
\(343\) | 1.50853e11 | 0.588479 | ||||||||
\(344\) | −3.80825e11 | −1.46627 | ||||||||
\(345\) | −3.43763e11 | −1.30639 | ||||||||
\(346\) | 3.23786e11 | 1.21455 | ||||||||
\(347\) | −1.69621e11 | −0.628054 | −0.314027 | − | 0.949414i | \(-0.601678\pi\) | ||||
−0.314027 | + | 0.949414i | \(0.601678\pi\) | |||||||
\(348\) | −5.28614e10 | −0.193211 | ||||||||
\(349\) | −3.05069e11 | −1.10074 | −0.550369 | − | 0.834922i | \(-0.685513\pi\) | ||||
−0.550369 | + | 0.834922i | \(0.685513\pi\) | |||||||
\(350\) | 2.12905e11 | 0.758367 | ||||||||
\(351\) | −5.20402e10 | −0.183002 | ||||||||
\(352\) | 2.70089e10 | 0.0937702 | ||||||||
\(353\) | −1.48766e10 | −0.0509938 | −0.0254969 | − | 0.999675i | \(-0.508117\pi\) | ||||
−0.0254969 | + | 0.999675i | \(0.508117\pi\) | |||||||
\(354\) | −4.33619e11 | −1.46755 | ||||||||
\(355\) | 3.40027e11 | 1.13628 | ||||||||
\(356\) | 1.85988e10 | 0.0613704 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.57329e11 | 1.79324 | ||||||||
\(359\) | −8.13885e10 | −0.258606 | −0.129303 | − | 0.991605i | \(-0.541274\pi\) | ||||
−0.129303 | + | 0.991605i | \(0.541274\pi\) | |||||||
\(360\) | 4.93866e11 | 1.54970 | ||||||||
\(361\) | −3.03760e11 | −0.941342 | ||||||||
\(362\) | 2.51118e11 | 0.768582 | ||||||||
\(363\) | 3.93572e11 | 1.18972 | ||||||||
\(364\) | 2.08857e10 | 0.0623580 | ||||||||
\(365\) | −1.11346e11 | −0.328366 | ||||||||
\(366\) | 9.52814e11 | 2.77551 | ||||||||
\(367\) | −2.76299e11 | −0.795028 | −0.397514 | − | 0.917596i | \(-0.630127\pi\) | ||||
−0.397514 | + | 0.917596i | \(0.630127\pi\) | |||||||
\(368\) | −2.02359e11 | −0.575185 | ||||||||
\(369\) | 1.77664e11 | 0.498861 | ||||||||
\(370\) | 7.24767e11 | 2.01044 | ||||||||
\(371\) | −3.04637e10 | −0.0834834 | ||||||||
\(372\) | −4.73412e10 | −0.128173 | ||||||||
\(373\) | 6.75562e10 | 0.180707 | 0.0903536 | − | 0.995910i | \(-0.471200\pi\) | ||||
0.0903536 | + | 0.995910i | \(0.471200\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.26778e12 | −3.31058 | ||||||||
\(376\) | 5.46558e11 | 1.41023 | ||||||||
\(377\) | −6.99803e11 | −1.78418 | ||||||||
\(378\) | 1.48230e10 | 0.0373441 | ||||||||
\(379\) | 2.28533e10 | 0.0568948 | 0.0284474 | − | 0.999595i | \(-0.490944\pi\) | ||||
0.0284474 | + | 0.999595i | \(0.490944\pi\) | |||||||
\(380\) | 2.25110e10 | 0.0553819 | ||||||||
\(381\) | −1.04930e12 | −2.55116 | ||||||||
\(382\) | −6.88741e11 | −1.65490 | ||||||||
\(383\) | 5.41458e11 | 1.28579 | 0.642896 | − | 0.765954i | \(-0.277733\pi\) | ||||
0.642896 | + | 0.765954i | \(0.277733\pi\) | |||||||
\(384\) | 6.76256e11 | 1.58716 | ||||||||
\(385\) | −9.10098e10 | −0.211113 | ||||||||
\(386\) | 2.53593e10 | 0.0581426 | ||||||||
\(387\) | −6.40084e11 | −1.45057 | ||||||||
\(388\) | 1.81963e10 | 0.0407607 | ||||||||
\(389\) | −2.43923e11 | −0.540107 | −0.270054 | − | 0.962845i | \(-0.587041\pi\) | ||||
−0.270054 | + | 0.962845i | \(0.587041\pi\) | |||||||
\(390\) | −1.96286e12 | −4.29635 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −3.92286e11 | −0.839104 | ||||||||
\(393\) | 5.37382e11 | 1.13636 | ||||||||
\(394\) | −3.57515e10 | −0.0747415 | ||||||||
\(395\) | −3.48563e11 | −0.720434 | ||||||||
\(396\) | 2.11768e10 | 0.0432744 | ||||||||
\(397\) | −6.74857e11 | −1.36350 | −0.681749 | − | 0.731586i | \(-0.738780\pi\) | ||||
−0.681749 | + | 0.731586i | \(0.738780\pi\) | |||||||
\(398\) | 3.01398e11 | 0.602096 | ||||||||
\(399\) | 5.24661e10 | 0.103634 | ||||||||
\(400\) | −1.31453e12 | −2.56744 | ||||||||
\(401\) | −3.75361e11 | −0.724937 | −0.362468 | − | 0.931996i | \(-0.618066\pi\) | ||||
−0.362468 | + | 0.931996i | \(0.618066\pi\) | |||||||
\(402\) | 2.49724e11 | 0.476918 | ||||||||
\(403\) | −6.26724e11 | −1.18360 | ||||||||
\(404\) | 1.42049e10 | 0.0265291 | ||||||||
\(405\) | −1.05996e12 | −1.95767 | ||||||||
\(406\) | 1.99330e11 | 0.364087 | ||||||||
\(407\) | −2.16309e11 | −0.390751 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.31772e11 | 1.11636 | 0.558182 | − | 0.829719i | \(-0.311499\pi\) | ||||
0.558182 | + | 0.829719i | \(0.311499\pi\) | |||||||
\(410\) | −6.00644e11 | −1.04976 | ||||||||
\(411\) | 5.94594e11 | 1.02786 | ||||||||
\(412\) | −6.77668e9 | −0.0115872 | ||||||||
\(413\) | 1.82482e11 | 0.308636 | ||||||||
\(414\) | −3.01623e11 | −0.504618 | ||||||||
\(415\) | −1.04492e12 | −1.72929 | ||||||||
\(416\) | −2.45144e11 | −0.401330 | ||||||||
\(417\) | −6.89795e11 | −1.11714 | ||||||||
\(418\) | −6.01991e10 | −0.0964488 | ||||||||
\(419\) | 5.81662e11 | 0.921951 | 0.460975 | − | 0.887413i | \(-0.347500\pi\) | ||||
0.460975 | + | 0.887413i | \(0.347500\pi\) | |||||||
\(420\) | 6.23974e10 | 0.0978463 | ||||||||
\(421\) | 3.73500e11 | 0.579457 | 0.289729 | − | 0.957109i | \(-0.406435\pi\) | ||||
0.289729 | + | 0.957109i | \(0.406435\pi\) | |||||||
\(422\) | −7.28698e11 | −1.11851 | ||||||||
\(423\) | 9.18645e11 | 1.39513 | ||||||||
\(424\) | 1.66801e11 | 0.250640 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.23430e11 | 0.917159 | ||||||||
\(427\) | −4.00979e11 | −0.583708 | ||||||||
\(428\) | −3.19508e10 | −0.0460241 | ||||||||
\(429\) | 5.85823e11 | 0.835042 | ||||||||
\(430\) | 2.16399e12 | 3.05244 | ||||||||
\(431\) | 1.32118e12 | 1.84423 | 0.922113 | − | 0.386920i | \(-0.126461\pi\) | ||||
0.922113 | + | 0.386920i | \(0.126461\pi\) | |||||||
\(432\) | −9.15208e10 | −0.126428 | ||||||||
\(433\) | 4.56730e11 | 0.624401 | 0.312201 | − | 0.950016i | \(-0.398934\pi\) | ||||
0.312201 | + | 0.950016i | \(0.398934\pi\) | |||||||
\(434\) | 1.78514e11 | 0.241529 | ||||||||
\(435\) | −2.09071e12 | −2.79958 | ||||||||
\(436\) | −4.09458e10 | −0.0542650 | ||||||||
\(437\) | 9.56917e10 | 0.125519 | ||||||||
\(438\) | −2.04151e11 | −0.265043 | ||||||||
\(439\) | 2.27163e11 | 0.291909 | 0.145954 | − | 0.989291i | \(-0.453375\pi\) | ||||
0.145954 | + | 0.989291i | \(0.453375\pi\) | |||||||
\(440\) | 4.98314e11 | 0.633820 | ||||||||
\(441\) | −6.59347e11 | −0.830119 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.03387e12 | 1.27541 | 0.637706 | − | 0.770280i | \(-0.279883\pi\) | ||||
0.637706 | + | 0.770280i | \(0.279883\pi\) | |||||||
\(444\) | 1.48304e11 | 0.181105 | ||||||||
\(445\) | 7.35595e11 | 0.889239 | ||||||||
\(446\) | −6.57271e11 | −0.786571 | ||||||||
\(447\) | 7.54094e11 | 0.893392 | ||||||||
\(448\) | −2.22560e11 | −0.261033 | ||||||||
\(449\) | 1.06299e12 | 1.23430 | 0.617150 | − | 0.786845i | \(-0.288287\pi\) | ||||
0.617150 | + | 0.786845i | \(0.288287\pi\) | |||||||
\(450\) | −1.95935e12 | −2.25245 | ||||||||
\(451\) | 1.79264e11 | 0.204032 | ||||||||
\(452\) | −6.13406e10 | −0.0691233 | ||||||||
\(453\) | −1.60959e12 | −1.79587 | ||||||||
\(454\) | 8.20712e11 | 0.906649 | ||||||||
\(455\) | 8.26044e11 | 0.903549 | ||||||||
\(456\) | −2.87272e11 | −0.311137 | ||||||||
\(457\) | −8.26432e10 | −0.0886307 | −0.0443154 | − | 0.999018i | \(-0.514111\pi\) | ||||
−0.0443154 | + | 0.999018i | \(0.514111\pi\) | |||||||
\(458\) | −8.21980e10 | −0.0872904 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.13805e11 | 0.118509 | ||||||||
\(461\) | 1.90976e11 | 0.196936 | 0.0984680 | − | 0.995140i | \(-0.468606\pi\) | ||||
0.0984680 | + | 0.995140i | \(0.468606\pi\) | |||||||
\(462\) | −1.66864e11 | −0.170402 | ||||||||
\(463\) | 9.16066e11 | 0.926429 | 0.463214 | − | 0.886246i | \(-0.346696\pi\) | ||||
0.463214 | + | 0.886246i | \(0.346696\pi\) | |||||||
\(464\) | −1.23071e12 | −1.23261 | ||||||||
\(465\) | −1.87238e12 | −1.85719 | ||||||||
\(466\) | 8.32571e11 | 0.817871 | ||||||||
\(467\) | 1.75288e12 | 1.70540 | 0.852701 | − | 0.522400i | \(-0.174963\pi\) | ||||
0.852701 | + | 0.522400i | \(0.174963\pi\) | |||||||
\(468\) | −1.92209e11 | −0.185211 | ||||||||
\(469\) | −1.05093e11 | −0.100299 | ||||||||
\(470\) | −3.10575e12 | −2.93580 | ||||||||
\(471\) | 2.24834e12 | 2.10508 | ||||||||
\(472\) | −9.99162e11 | −0.926610 | ||||||||
\(473\) | −6.45850e11 | −0.593276 | ||||||||
\(474\) | −6.39081e11 | −0.581505 | ||||||||
\(475\) | 6.21616e11 | 0.560275 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.80355e11 | 0.247957 | ||||||||
\(478\) | −1.64225e12 | −1.43885 | ||||||||
\(479\) | 8.05193e11 | 0.698860 | 0.349430 | − | 0.936963i | \(-0.386375\pi\) | ||||
0.349430 | + | 0.936963i | \(0.386375\pi\) | |||||||
\(480\) | −7.32385e11 | −0.629730 | ||||||||
\(481\) | 1.96331e12 | 1.67239 | ||||||||
\(482\) | −6.90395e11 | −0.582620 | ||||||||
\(483\) | 2.65245e11 | 0.221761 | ||||||||
\(484\) | −1.30295e11 | −0.107925 | ||||||||
\(485\) | 7.19679e11 | 0.590610 | ||||||||
\(486\) | −1.79476e12 | −1.45929 | ||||||||
\(487\) | 2.02412e11 | 0.163063 | 0.0815315 | − | 0.996671i | \(-0.474019\pi\) | ||||
0.0815315 | + | 0.996671i | \(0.474019\pi\) | |||||||
\(488\) | 2.19551e12 | 1.75245 | ||||||||
\(489\) | −1.37275e12 | −1.08568 | ||||||||
\(490\) | 2.22912e12 | 1.74683 | ||||||||
\(491\) | −1.40366e12 | −1.08992 | −0.544960 | − | 0.838462i | \(-0.683455\pi\) | ||||
−0.544960 | + | 0.838462i | \(0.683455\pi\) | |||||||
\(492\) | −1.22905e11 | −0.0945645 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 5.46393e11 | 0.412794 | ||||||||
\(495\) | 8.37557e11 | 0.627034 | ||||||||
\(496\) | −1.10219e12 | −0.817692 | ||||||||
\(497\) | −2.62362e11 | −0.192884 | ||||||||
\(498\) | −1.91583e12 | −1.39581 | ||||||||
\(499\) | 1.34731e12 | 0.972784 | 0.486392 | − | 0.873741i | \(-0.338313\pi\) | ||||
0.486392 | + | 0.873741i | \(0.338313\pi\) | |||||||
\(500\) | 4.19708e11 | 0.300319 | ||||||||
\(501\) | 1.84863e12 | 1.31093 | ||||||||
\(502\) | −1.21973e12 | −0.857228 | ||||||||
\(503\) | 9.70190e11 | 0.675773 | 0.337887 | − | 0.941187i | \(-0.390288\pi\) | ||||
0.337887 | + | 0.941187i | \(0.390288\pi\) | |||||||
\(504\) | −3.81062e11 | −0.263062 | ||||||||
\(505\) | 5.61816e11 | 0.384400 | ||||||||
\(506\) | −3.04340e11 | −0.206386 | ||||||||
\(507\) | −3.25687e12 | −2.18910 | ||||||||
\(508\) | 3.47378e11 | 0.231428 | ||||||||
\(509\) | −4.58129e11 | −0.302523 | −0.151261 | − | 0.988494i | \(-0.548334\pi\) | ||||
−0.151261 | + | 0.988494i | \(0.548334\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.59139e10 | 0.0557403 | ||||||||
\(512\) | 1.16980e12 | 0.752311 | ||||||||
\(513\) | 4.32785e10 | 0.0275895 | ||||||||
\(514\) | −1.06580e12 | −0.673506 | ||||||||
\(515\) | −2.68023e11 | −0.167896 | ||||||||
\(516\) | 4.42802e11 | 0.274970 | ||||||||
\(517\) | 9.26920e11 | 0.570604 | ||||||||
\(518\) | −5.59224e11 | −0.341273 | ||||||||
\(519\) | 2.62039e12 | 1.58531 | ||||||||
\(520\) | −4.52291e12 | −2.71271 | ||||||||
\(521\) | 9.79258e11 | 0.582274 | 0.291137 | − | 0.956681i | \(-0.405966\pi\) | ||||
0.291137 | + | 0.956681i | \(0.405966\pi\) | |||||||
\(522\) | −1.83442e12 | −1.08139 | ||||||||
\(523\) | −1.82449e12 | −1.06631 | −0.533157 | − | 0.846016i | \(-0.678994\pi\) | ||||
−0.533157 | + | 0.846016i | \(0.678994\pi\) | |||||||
\(524\) | −1.77904e11 | −0.103085 | ||||||||
\(525\) | 1.72304e12 | 0.989869 | ||||||||
\(526\) | −1.06927e12 | −0.609048 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 1.03026e12 | 0.576892 | ||||||||
\(529\) | −1.31738e12 | −0.731409 | ||||||||
\(530\) | −9.47823e11 | −0.521778 | ||||||||
\(531\) | −1.67937e12 | −0.916689 | ||||||||
\(532\) | −1.73693e10 | −0.00940110 | ||||||||
\(533\) | −1.62708e12 | −0.873243 | ||||||||
\(534\) | 1.34869e12 | 0.717757 | ||||||||
\(535\) | −1.26368e12 | −0.666876 | ||||||||
\(536\) | 5.75425e11 | 0.301125 | ||||||||
\(537\) | 4.51046e12 | 2.34065 | ||||||||
\(538\) | 1.86207e12 | 0.958242 | ||||||||
\(539\) | −6.65286e11 | −0.339515 | ||||||||
\(540\) | 5.14706e10 | 0.0260488 | ||||||||
\(541\) | 2.54541e12 | 1.27753 | 0.638763 | − | 0.769403i | \(-0.279446\pi\) | ||||
0.638763 | + | 0.769403i | \(0.279446\pi\) | |||||||
\(542\) | −4.91502e11 | −0.244641 | ||||||||
\(543\) | 2.03230e12 | 1.00320 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.61944e12 | −0.786285 | ||||||||
\(546\) | 1.51453e12 | 0.729307 | ||||||||
\(547\) | 7.76701e11 | 0.370946 | 0.185473 | − | 0.982649i | \(-0.440618\pi\) | ||||
0.185473 | + | 0.982649i | \(0.440618\pi\) | |||||||
\(548\) | −1.96844e11 | −0.0932417 | ||||||||
\(549\) | 3.69018e12 | 1.73369 | ||||||||
\(550\) | −1.97700e12 | −0.921243 | ||||||||
\(551\) | 5.81981e11 | 0.268984 | ||||||||
\(552\) | −1.45232e12 | −0.665788 | ||||||||
\(553\) | 2.68948e11 | 0.122294 | ||||||||
\(554\) | 2.19258e12 | 0.988922 | ||||||||
\(555\) | 5.86553e12 | 2.62415 | ||||||||
\(556\) | 2.28361e11 | 0.101341 | ||||||||
\(557\) | 1.13490e12 | 0.499586 | 0.249793 | − | 0.968299i | \(-0.419637\pi\) | ||||
0.249793 | + | 0.968299i | \(0.419637\pi\) | |||||||
\(558\) | −1.64285e12 | −0.717373 | ||||||||
\(559\) | 5.86201e12 | 2.53918 | ||||||||
\(560\) | 1.45273e12 | 0.624221 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.81824e12 | −1.61455 | ||||||||
\(563\) | 6.84519e11 | 0.287143 | 0.143571 | − | 0.989640i | \(-0.454141\pi\) | ||||
0.143571 | + | 0.989640i | \(0.454141\pi\) | |||||||
\(564\) | −6.35507e11 | −0.264463 | ||||||||
\(565\) | −2.42607e12 | −1.00158 | ||||||||
\(566\) | 1.18548e12 | 0.485534 | ||||||||
\(567\) | 8.17853e11 | 0.332316 | ||||||||
\(568\) | 1.43653e12 | 0.579092 | ||||||||
\(569\) | 4.27388e11 | 0.170930 | 0.0854648 | − | 0.996341i | \(-0.472762\pi\) | ||||
0.0854648 | + | 0.996341i | \(0.472762\pi\) | |||||||
\(570\) | 1.63239e12 | 0.647719 | ||||||||
\(571\) | 3.34538e12 | 1.31699 | 0.658496 | − | 0.752584i | \(-0.271193\pi\) | ||||
0.658496 | + | 0.752584i | \(0.271193\pi\) | |||||||
\(572\) | −1.93941e11 | −0.0757507 | ||||||||
\(573\) | −5.57397e12 | −2.16008 | ||||||||
\(574\) | 4.63451e11 | 0.178197 | ||||||||
\(575\) | 3.14261e12 | 1.19891 | ||||||||
\(576\) | 2.04820e12 | 0.775303 | ||||||||
\(577\) | −6.11445e10 | −0.0229650 | −0.0114825 | − | 0.999934i | \(-0.503655\pi\) | ||||
−0.0114825 | + | 0.999934i | \(0.503655\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.05233e11 | 0.0758914 | ||||||||
\(580\) | 6.92143e11 | 0.253963 | ||||||||
\(581\) | 8.06251e11 | 0.293547 | ||||||||
\(582\) | 1.31951e12 | 0.476716 | ||||||||
\(583\) | 2.82881e11 | 0.101413 | ||||||||
\(584\) | −4.70412e11 | −0.167348 | ||||||||
\(585\) | −7.60202e12 | −2.68366 | ||||||||
\(586\) | −2.27202e12 | −0.795925 | ||||||||
\(587\) | −1.97678e12 | −0.687206 | −0.343603 | − | 0.939115i | \(-0.611648\pi\) | ||||
−0.343603 | + | 0.939115i | \(0.611648\pi\) | |||||||
\(588\) | 4.56128e11 | 0.157358 | ||||||||
\(589\) | 5.21206e11 | 0.178439 | ||||||||
\(590\) | 5.67761e12 | 1.92900 | ||||||||
\(591\) | −2.89337e11 | −0.0975573 | ||||||||
\(592\) | 3.45279e12 | 1.15537 | ||||||||
\(593\) | −2.58955e12 | −0.859959 | −0.429980 | − | 0.902839i | \(-0.641479\pi\) | ||||
−0.429980 | + | 0.902839i | \(0.641479\pi\) | |||||||
\(594\) | −1.37644e11 | −0.0453646 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.49648e11 | −0.0810438 | ||||||||
\(597\) | 2.43921e12 | 0.785894 | ||||||||
\(598\) | 2.76232e12 | 0.883320 | ||||||||
\(599\) | 2.28277e12 | 0.724507 | 0.362253 | − | 0.932080i | \(-0.382008\pi\) | ||||
0.362253 | + | 0.932080i | \(0.382008\pi\) | |||||||
\(600\) | −9.43429e12 | −2.97186 | ||||||||
\(601\) | 3.16197e12 | 0.988603 | 0.494302 | − | 0.869290i | \(-0.335424\pi\) | ||||
0.494302 | + | 0.869290i | \(0.335424\pi\) | |||||||
\(602\) | −1.66972e12 | −0.518154 | ||||||||
\(603\) | 9.67163e11 | 0.297901 | ||||||||
\(604\) | 5.32866e11 | 0.162912 | ||||||||
\(605\) | −5.15325e12 | −1.56380 | ||||||||
\(606\) | 1.03007e12 | 0.310271 | ||||||||
\(607\) | 2.56502e12 | 0.766906 | 0.383453 | − | 0.923560i | \(-0.374735\pi\) | ||||
0.383453 | + | 0.923560i | \(0.374735\pi\) | |||||||
\(608\) | 2.03870e11 | 0.0605046 | ||||||||
\(609\) | 1.61317e12 | 0.475229 | ||||||||
\(610\) | −1.24757e13 | −3.64822 | ||||||||
\(611\) | −8.41312e12 | −2.44215 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.33870e12 | −0.382923 | −0.191461 | − | 0.981500i | \(-0.561323\pi\) | ||||
−0.191461 | + | 0.981500i | \(0.561323\pi\) | |||||||
\(614\) | −4.58630e12 | −1.30228 | ||||||||
\(615\) | −4.86100e12 | −1.37021 | ||||||||
\(616\) | −3.84495e11 | −0.107591 | ||||||||
\(617\) | 3.94532e11 | 0.109597 | 0.0547985 | − | 0.998497i | \(-0.482548\pi\) | ||||
0.0547985 | + | 0.998497i | \(0.482548\pi\) | |||||||
\(618\) | −4.91412e11 | −0.135518 | ||||||||
\(619\) | 4.29120e12 | 1.17482 | 0.587410 | − | 0.809290i | \(-0.300148\pi\) | ||||
0.587410 | + | 0.809290i | \(0.300148\pi\) | |||||||
\(620\) | 6.19864e11 | 0.168474 | ||||||||
\(621\) | 2.18796e11 | 0.0590375 | ||||||||
\(622\) | 4.37743e12 | 1.17264 | ||||||||
\(623\) | −5.67579e11 | −0.150949 | ||||||||
\(624\) | −9.35109e12 | −2.46906 | ||||||||
\(625\) | 7.77509e12 | 2.03819 | ||||||||
\(626\) | −5.20548e12 | −1.35480 | ||||||||
\(627\) | −4.87191e11 | −0.125891 | ||||||||
\(628\) | −7.44330e11 | −0.190962 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 2.16534e12 | 0.547638 | ||||||||
\(631\) | −2.10436e12 | −0.528431 | −0.264215 | − | 0.964464i | \(-0.585113\pi\) | ||||
−0.264215 | + | 0.964464i | \(0.585113\pi\) | |||||||
\(632\) | −1.47259e12 | −0.367161 | ||||||||
\(633\) | −5.89735e12 | −1.45996 | ||||||||
\(634\) | −5.74481e12 | −1.41213 | ||||||||
\(635\) | 1.37391e13 | 3.35332 | ||||||||
\(636\) | −1.93946e11 | −0.0470028 | ||||||||
\(637\) | 6.03842e12 | 1.45310 | ||||||||
\(638\) | −1.85094e12 | −0.442282 | ||||||||
\(639\) | 2.41450e12 | 0.572892 | ||||||||
\(640\) | −8.85459e12 | −2.08621 | ||||||||
\(641\) | −4.70391e12 | −1.10052 | −0.550260 | − | 0.834993i | \(-0.685472\pi\) | ||||
−0.550260 | + | 0.834993i | \(0.685472\pi\) | |||||||
\(642\) | −2.31692e12 | −0.538275 | ||||||||
\(643\) | −2.97950e12 | −0.687376 | −0.343688 | − | 0.939084i | \(-0.611676\pi\) | ||||
−0.343688 | + | 0.939084i | \(0.611676\pi\) | |||||||
\(644\) | −8.78111e10 | −0.0201170 | ||||||||
\(645\) | 1.75132e13 | 3.98424 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.15794e11 | −0.138155 | −0.0690774 | − | 0.997611i | \(-0.522006\pi\) | ||||
−0.0690774 | + | 0.997611i | \(0.522006\pi\) | |||||||
\(648\) | −4.47806e12 | −0.997706 | ||||||||
\(649\) | −1.69450e12 | −0.374922 | ||||||||
\(650\) | 1.79441e13 | 3.94285 | ||||||||
\(651\) | 1.44471e12 | 0.315259 | ||||||||
\(652\) | 4.54458e11 | 0.0984871 | ||||||||
\(653\) | −6.22513e12 | −1.33980 | −0.669899 | − | 0.742453i | \(-0.733662\pi\) | ||||
−0.669899 | + | 0.742453i | \(0.733662\pi\) | |||||||
\(654\) | −2.96919e12 | −0.634656 | ||||||||
\(655\) | −7.03624e12 | −1.49367 | ||||||||
\(656\) | −2.86147e12 | −0.603284 | ||||||||
\(657\) | −7.90660e11 | −0.165556 | ||||||||
\(658\) | 2.39637e12 | 0.498353 | ||||||||
\(659\) | 5.49448e12 | 1.13486 | 0.567430 | − | 0.823421i | \(-0.307938\pi\) | ||||
0.567430 | + | 0.823421i | \(0.307938\pi\) | |||||||
\(660\) | −5.79411e11 | −0.118861 | ||||||||
\(661\) | −2.29988e11 | −0.0468596 | −0.0234298 | − | 0.999725i | \(-0.507459\pi\) | ||||
−0.0234298 | + | 0.999725i | \(0.507459\pi\) | |||||||
\(662\) | 6.46976e12 | 1.30926 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.41454e12 | −0.881310 | ||||||||
\(665\) | −6.86967e11 | −0.136219 | ||||||||
\(666\) | 5.14650e12 | 1.01363 | ||||||||
\(667\) | 2.94223e12 | 0.575586 | ||||||||
\(668\) | −6.12002e11 | −0.118921 | ||||||||
\(669\) | −5.31929e12 | −1.02668 | ||||||||
\(670\) | −3.26978e12 | −0.626876 | ||||||||
\(671\) | 3.72342e12 | 0.709072 | ||||||||
\(672\) | 5.65102e11 | 0.106897 | ||||||||
\(673\) | −9.70100e11 | −0.182284 | −0.0911420 | − | 0.995838i | \(-0.529052\pi\) | ||||
−0.0911420 | + | 0.995838i | \(0.529052\pi\) | |||||||
\(674\) | −4.53401e12 | −0.846277 | ||||||||
\(675\) | 1.42131e12 | 0.263524 | ||||||||
\(676\) | 1.07821e12 | 0.198584 | ||||||||
\(677\) | 5.03955e12 | 0.922026 | 0.461013 | − | 0.887393i | \(-0.347486\pi\) | ||||
0.461013 | + | 0.887393i | \(0.347486\pi\) | |||||||
\(678\) | −4.44813e12 | −0.808432 | ||||||||
\(679\) | −5.55298e11 | −0.100256 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.64201e12 | 1.18342 | ||||||||
\(682\) | −1.65765e12 | −0.293402 | ||||||||
\(683\) | 5.01528e12 | 0.881864 | 0.440932 | − | 0.897540i | \(-0.354648\pi\) | ||||
0.440932 | + | 0.897540i | \(0.354648\pi\) | |||||||
\(684\) | 1.59848e11 | 0.0279225 | ||||||||
\(685\) | −7.78534e12 | −1.35105 | ||||||||
\(686\) | −3.62148e12 | −0.624349 | ||||||||
\(687\) | −6.65227e11 | −0.113937 | ||||||||
\(688\) | 1.03093e13 | 1.75420 | ||||||||
\(689\) | −2.56754e12 | −0.434042 | ||||||||
\(690\) | 8.25261e12 | 1.38602 | ||||||||
\(691\) | 2.82622e12 | 0.471580 | 0.235790 | − | 0.971804i | \(-0.424232\pi\) | ||||
0.235790 | + | 0.971804i | \(0.424232\pi\) | |||||||
\(692\) | −8.67498e11 | −0.143811 | ||||||||
\(693\) | −6.46252e11 | −0.106439 | ||||||||
\(694\) | 4.07203e12 | 0.666336 | ||||||||
\(695\) | 9.03187e12 | 1.46841 | ||||||||
\(696\) | −8.83275e12 | −1.42677 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 7.32369e12 | 1.16783 | ||||||||
\(699\) | 6.73799e12 | 1.06754 | ||||||||
\(700\) | −5.70423e11 | −0.0897958 | ||||||||
\(701\) | 2.11841e12 | 0.331343 | 0.165672 | − | 0.986181i | \(-0.447021\pi\) | ||||
0.165672 | + | 0.986181i | \(0.447021\pi\) | |||||||
\(702\) | 1.24931e12 | 0.194157 | ||||||||
\(703\) | −1.63276e12 | −0.252129 | ||||||||
\(704\) | 2.06665e12 | 0.317095 | ||||||||
\(705\) | −2.51348e13 | −3.83199 | ||||||||
\(706\) | 3.57137e11 | 0.0541021 | ||||||||
\(707\) | −4.33492e11 | −0.0652520 | ||||||||
\(708\) | 1.16177e12 | 0.173768 | ||||||||
\(709\) | −1.08197e13 | −1.60808 | −0.804039 | − | 0.594576i | \(-0.797320\pi\) | ||||
−0.804039 | + | 0.594576i | \(0.797320\pi\) | |||||||
\(710\) | −8.16291e12 | −1.20554 | ||||||||
\(711\) | −2.47511e12 | −0.363230 | ||||||||
\(712\) | 3.10771e12 | 0.453190 | ||||||||
\(713\) | 2.63498e12 | 0.381834 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.67050e12 | −1.09761 | ||||||||
\(716\) | −1.49322e12 | −0.212332 | ||||||||
\(717\) | −1.32907e13 | −1.87808 | ||||||||
\(718\) | 1.95387e12 | 0.274369 | ||||||||
\(719\) | 2.57986e12 | 0.360011 | 0.180006 | − | 0.983666i | \(-0.442388\pi\) | ||||
0.180006 | + | 0.983666i | \(0.442388\pi\) | |||||||
\(720\) | −1.33694e13 | −1.85402 | ||||||||
\(721\) | 2.06804e11 | 0.0285004 | ||||||||
\(722\) | 7.29225e12 | 0.998721 | ||||||||
\(723\) | −5.58736e12 | −0.760473 | ||||||||
\(724\) | −6.72806e11 | −0.0910052 | ||||||||
\(725\) | 1.91128e13 | 2.56923 | ||||||||
\(726\) | −9.44834e12 | −1.26224 | ||||||||
\(727\) | −4.66836e11 | −0.0619811 | −0.0309905 | − | 0.999520i | \(-0.509866\pi\) | ||||
−0.0309905 | + | 0.999520i | \(0.509866\pi\) | |||||||
\(728\) | 3.48984e12 | 0.460483 | ||||||||
\(729\) | −6.32368e12 | −0.829271 | ||||||||
\(730\) | 2.67306e12 | 0.348381 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −2.55282e12 | −0.328639 | ||||||||
\(733\) | −8.68081e12 | −1.11069 | −0.555344 | − | 0.831621i | \(-0.687414\pi\) | ||||
−0.555344 | + | 0.831621i | \(0.687414\pi\) | |||||||
\(734\) | 6.63302e12 | 0.843488 | ||||||||
\(735\) | 1.80402e13 | 2.28007 | ||||||||
\(736\) | 1.03068e12 | 0.129471 | ||||||||
\(737\) | 9.75875e11 | 0.121840 | ||||||||
\(738\) | −4.26511e12 | −0.529269 | ||||||||
\(739\) | 1.36517e13 | 1.68379 | 0.841894 | − | 0.539643i | \(-0.181441\pi\) | ||||
0.841894 | + | 0.539643i | \(0.181441\pi\) | |||||||
\(740\) | −1.94182e12 | −0.238049 | ||||||||
\(741\) | 4.42195e12 | 0.538805 | ||||||||
\(742\) | 7.31332e11 | 0.0885721 | ||||||||
\(743\) | −5.41571e12 | −0.651937 | −0.325968 | − | 0.945381i | \(-0.605690\pi\) | ||||
−0.325968 | + | 0.945381i | \(0.605690\pi\) | |||||||
\(744\) | −7.91036e12 | −0.946495 | ||||||||
\(745\) | −9.87377e12 | −1.17430 | ||||||||
\(746\) | −1.62180e12 | −0.191722 | ||||||||
\(747\) | −7.41987e12 | −0.871874 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.75045e11 | 0.113203 | ||||||||
\(750\) | 3.04352e13 | 3.51237 | ||||||||
\(751\) | 4.96526e12 | 0.569590 | 0.284795 | − | 0.958588i | \(-0.408074\pi\) | ||||
0.284795 | + | 0.958588i | \(0.408074\pi\) | |||||||
\(752\) | −1.47958e13 | −1.68717 | ||||||||
\(753\) | −9.87125e12 | −1.11891 | ||||||||
\(754\) | 1.67999e13 | 1.89294 | ||||||||
\(755\) | 2.10753e13 | 2.36054 | ||||||||
\(756\) | −3.97143e10 | −0.00442179 | ||||||||
\(757\) | 1.38118e13 | 1.52869 | 0.764343 | − | 0.644810i | \(-0.223064\pi\) | ||||
0.764343 | + | 0.644810i | \(0.223064\pi\) | |||||||
\(758\) | −5.48631e11 | −0.0603627 | ||||||||
\(759\) | −2.46302e12 | −0.269389 | ||||||||
\(760\) | 3.76141e12 | 0.408968 | ||||||||
\(761\) | 1.56510e13 | 1.69166 | 0.845828 | − | 0.533455i | \(-0.179107\pi\) | ||||
0.845828 | + | 0.533455i | \(0.179107\pi\) | |||||||
\(762\) | 2.51902e13 | 2.70666 | ||||||||
\(763\) | 1.24954e12 | 0.133472 | ||||||||
\(764\) | 1.84530e12 | 0.195951 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.29986e13 | −1.36417 | ||||||||
\(767\) | 1.53800e13 | 1.60464 | ||||||||
\(768\) | −4.95562e12 | −0.514011 | ||||||||
\(769\) | −4.07932e11 | −0.0420648 | −0.0210324 | − | 0.999779i | \(-0.506695\pi\) | ||||
−0.0210324 | + | 0.999779i | \(0.506695\pi\) | |||||||
\(770\) | 2.18484e12 | 0.223981 | ||||||||
\(771\) | −8.62550e12 | −0.879102 | ||||||||
\(772\) | −6.79436e10 | −0.00688447 | ||||||||
\(773\) | 2.25431e11 | 0.0227094 | 0.0113547 | − | 0.999936i | \(-0.496386\pi\) | ||||
0.0113547 | + | 0.999936i | \(0.496386\pi\) | |||||||
\(774\) | 1.53663e13 | 1.53899 | ||||||||
\(775\) | 1.71169e13 | 1.70438 | ||||||||
\(776\) | 3.04047e12 | 0.300998 | ||||||||
\(777\) | −4.52579e12 | −0.445451 | ||||||||
\(778\) | 5.85578e12 | 0.573029 | ||||||||
\(779\) | 1.35313e12 | 0.131650 | ||||||||
\(780\) | 5.25898e12 | 0.508716 | ||||||||
\(781\) | 2.43625e12 | 0.234310 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.33068e12 | 0.126516 | ||||||||
\(784\) | 1.06195e13 | 1.00388 | ||||||||
\(785\) | −2.94388e13 | −2.76698 | ||||||||
\(786\) | −1.29008e13 | −1.20563 | ||||||||
\(787\) | 1.53299e13 | 1.42446 | 0.712232 | − | 0.701944i | \(-0.247684\pi\) | ||||
0.712232 | + | 0.701944i | \(0.247684\pi\) | |||||||
\(788\) | 9.57868e10 | 0.00884989 | ||||||||
\(789\) | −8.65359e12 | −0.794968 | ||||||||
\(790\) | 8.36783e12 | 0.764348 | ||||||||
\(791\) | 1.87193e12 | 0.170018 | ||||||||
\(792\) | 3.53848e12 | 0.319560 | ||||||||
\(793\) | −3.37953e13 | −3.03478 | ||||||||
\(794\) | 1.62011e13 | 1.44661 | ||||||||
\(795\) | −7.67072e12 | −0.681058 | ||||||||
\(796\) | −8.07516e11 | −0.0712922 | ||||||||
\(797\) | −5.72337e12 | −0.502446 | −0.251223 | − | 0.967929i | \(-0.580833\pi\) | ||||
−0.251223 | + | 0.967929i | \(0.580833\pi\) | |||||||
\(798\) | −1.25954e12 | −0.109951 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 6.69530e12 | 0.577917 | ||||||||
\(801\) | 5.22338e12 | 0.448338 | ||||||||
\(802\) | 9.01117e12 | 0.769125 | ||||||||
\(803\) | −7.97781e11 | −0.0677117 | ||||||||
\(804\) | −6.69071e11 | −0.0564703 | ||||||||
\(805\) | −3.47300e12 | −0.291489 | ||||||||
\(806\) | 1.50455e13 | 1.25574 | ||||||||
\(807\) | 1.50697e13 | 1.25076 | ||||||||
\(808\) | 2.37354e12 | 0.195905 | ||||||||
\(809\) | 3.52847e12 | 0.289613 | 0.144807 | − | 0.989460i | \(-0.453744\pi\) | ||||
0.144807 | + | 0.989460i | \(0.453744\pi\) | |||||||
\(810\) | 2.54460e13 | 2.07700 | ||||||||
\(811\) | 1.52284e13 | 1.23612 | 0.618058 | − | 0.786133i | \(-0.287920\pi\) | ||||
0.618058 | + | 0.786133i | \(0.287920\pi\) | |||||||
\(812\) | −5.34052e11 | −0.0431103 | ||||||||
\(813\) | −3.97772e12 | −0.319321 | ||||||||
\(814\) | 5.19286e12 | 0.414569 | ||||||||
\(815\) | 1.79742e13 | 1.42705 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.87505e12 | −0.382807 | ||||||||
\(818\) | −1.51667e13 | −1.18441 | ||||||||
\(819\) | 5.86565e12 | 0.455553 | ||||||||
\(820\) | 1.60927e12 | 0.124298 | ||||||||
\(821\) | 2.18898e13 | 1.68150 | 0.840752 | − | 0.541420i | \(-0.182113\pi\) | ||||
0.840752 | + | 0.541420i | \(0.182113\pi\) | |||||||
\(822\) | −1.42742e13 | −1.09051 | ||||||||
\(823\) | 1.41049e13 | 1.07169 | 0.535846 | − | 0.844316i | \(-0.319993\pi\) | ||||
0.535846 | + | 0.844316i | \(0.319993\pi\) | |||||||
\(824\) | −1.13233e12 | −0.0855660 | ||||||||
\(825\) | −1.59998e13 | −1.20246 | ||||||||
\(826\) | −4.38079e12 | −0.327448 | ||||||||
\(827\) | 1.50447e12 | 0.111843 | 0.0559216 | − | 0.998435i | \(-0.482190\pi\) | ||||
0.0559216 | + | 0.998435i | \(0.482190\pi\) | |||||||
\(828\) | 8.08119e11 | 0.0597501 | ||||||||
\(829\) | 1.36965e13 | 1.00720 | 0.503600 | − | 0.863937i | \(-0.332009\pi\) | ||||
0.503600 | + | 0.863937i | \(0.332009\pi\) | |||||||
\(830\) | 2.50850e13 | 1.83469 | ||||||||
\(831\) | 1.77445e13 | 1.29080 | ||||||||
\(832\) | −1.87578e13 | −1.35715 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.65597e13 | 1.18524 | ||||||||
\(835\) | −2.42051e13 | −1.72313 | ||||||||
\(836\) | 1.61288e11 | 0.0114202 | ||||||||
\(837\) | 1.19172e12 | 0.0839286 | ||||||||
\(838\) | −1.39638e13 | −0.978148 | ||||||||
\(839\) | −1.29771e12 | −0.0904170 | −0.0452085 | − | 0.998978i | \(-0.514395\pi\) | ||||
−0.0452085 | + | 0.998978i | \(0.514395\pi\) | |||||||
\(840\) | 1.04261e13 | 0.722548 | ||||||||
\(841\) | 3.38699e12 | 0.233470 | ||||||||
\(842\) | −8.96649e12 | −0.614778 | ||||||||
\(843\) | −3.09010e13 | −2.10741 | ||||||||
\(844\) | 1.95236e12 | 0.132440 | ||||||||
\(845\) | 4.26440e13 | 2.87742 | ||||||||
\(846\) | −2.20536e13 | −1.48017 | ||||||||
\(847\) | 3.97620e12 | 0.265456 | ||||||||
\(848\) | −4.51543e12 | −0.299859 | ||||||||
\(849\) | 9.59407e12 | 0.633750 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.25450e12 | −0.539520 | ||||||||
\(852\) | −1.67032e12 | −0.108598 | ||||||||
\(853\) | 8.68335e12 | 0.561587 | 0.280793 | − | 0.959768i | \(-0.409402\pi\) | ||||
0.280793 | + | 0.959768i | \(0.409402\pi\) | |||||||
\(854\) | 9.62615e12 | 0.619288 | ||||||||
\(855\) | 6.32211e12 | 0.404589 | ||||||||
\(856\) | −5.33875e12 | −0.339866 | ||||||||
\(857\) | 1.27598e13 | 0.808034 | 0.404017 | − | 0.914751i | \(-0.367614\pi\) | ||||
0.404017 | + | 0.914751i | \(0.367614\pi\) | |||||||
\(858\) | −1.40636e13 | −0.885942 | ||||||||
\(859\) | 2.56569e12 | 0.160781 | 0.0803905 | − | 0.996763i | \(-0.474383\pi\) | ||||
0.0803905 | + | 0.996763i | \(0.474383\pi\) | |||||||
\(860\) | −5.79785e12 | −0.361430 | ||||||||
\(861\) | 3.75071e12 | 0.232594 | ||||||||
\(862\) | −3.17171e13 | −1.95664 | ||||||||
\(863\) | −2.29743e13 | −1.40992 | −0.704960 | − | 0.709247i | \(-0.749035\pi\) | ||||
−0.704960 | + | 0.709247i | \(0.749035\pi\) | |||||||
\(864\) | 4.66144e11 | 0.0284582 | ||||||||
\(865\) | −3.43102e13 | −2.08378 | ||||||||
\(866\) | −1.09646e13 | −0.662461 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.78282e11 | −0.0285986 | ||||||||
\(869\) | −2.49740e12 | −0.148559 | ||||||||
\(870\) | 5.01910e13 | 2.97022 | ||||||||
\(871\) | −8.85745e12 | −0.521467 | ||||||||
\(872\) | −6.84173e12 | −0.400721 | ||||||||
\(873\) | 5.11037e12 | 0.297775 | ||||||||
\(874\) | −2.29724e12 | −0.133169 | ||||||||
\(875\) | −1.28082e13 | −0.738674 | ||||||||
\(876\) | 5.46968e11 | 0.0313829 | ||||||||
\(877\) | −2.71354e13 | −1.54895 | −0.774475 | − | 0.632604i | \(-0.781986\pi\) | ||||
−0.774475 | + | 0.632604i | \(0.781986\pi\) | |||||||
\(878\) | −5.45342e12 | −0.309702 | ||||||||
\(879\) | −1.83874e13 | −1.03889 | ||||||||
\(880\) | −1.34898e13 | −0.758285 | ||||||||
\(881\) | −8.69256e12 | −0.486134 | −0.243067 | − | 0.970009i | \(-0.578154\pi\) | ||||
−0.243067 | + | 0.970009i | \(0.578154\pi\) | |||||||
\(882\) | 1.58287e13 | 0.880719 | ||||||||
\(883\) | 1.44572e13 | 0.800318 | 0.400159 | − | 0.916446i | \(-0.368955\pi\) | ||||
0.400159 | + | 0.916446i | \(0.368955\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.59488e13 | 2.51785 | ||||||||
\(886\) | −2.48199e13 | −1.35315 | ||||||||
\(887\) | −2.51921e13 | −1.36649 | −0.683246 | − | 0.730188i | \(-0.739433\pi\) | ||||
−0.683246 | + | 0.730188i | \(0.739433\pi\) | |||||||
\(888\) | 2.47805e13 | 1.33737 | ||||||||
\(889\) | −1.06009e13 | −0.569228 | ||||||||
\(890\) | −1.76592e13 | −0.943442 | ||||||||
\(891\) | −7.59444e12 | −0.403688 | ||||||||
\(892\) | 1.76099e12 | 0.0931352 | ||||||||
\(893\) | 6.99664e12 | 0.368178 | ||||||||
\(894\) | −1.81033e13 | −0.947848 | ||||||||
\(895\) | −5.90579e13 | −3.07662 | ||||||||
\(896\) | 6.83213e12 | 0.354136 | ||||||||
\(897\) | 2.23554e13 | 1.15296 | ||||||||
\(898\) | −2.55188e13 | −1.30954 | ||||||||
\(899\) | 1.60255e13 | 0.818263 | ||||||||
\(900\) | 5.24956e12 | 0.266705 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −4.30353e12 | −0.216469 | ||||||||
\(903\) | −1.35130e13 | −0.676327 | ||||||||
\(904\) | −1.02495e13 | −0.510442 | ||||||||
\(905\) | −2.66100e13 | −1.31864 | ||||||||
\(906\) | 3.86409e13 | 1.90533 | ||||||||
\(907\) | 3.05227e13 | 1.49758 | 0.748790 | − | 0.662807i | \(-0.230635\pi\) | ||||
0.748790 | + | 0.662807i | \(0.230635\pi\) | |||||||
\(908\) | −2.19888e12 | −0.107353 | ||||||||
\(909\) | 3.98940e12 | 0.193807 | ||||||||
\(910\) | −1.98306e13 | −0.958625 | ||||||||
\(911\) | 3.56835e13 | 1.71646 | 0.858231 | − | 0.513264i | \(-0.171564\pi\) | ||||
0.858231 | + | 0.513264i | \(0.171564\pi\) | |||||||
\(912\) | 7.77669e12 | 0.372236 | ||||||||
\(913\) | −7.48671e12 | −0.356593 | ||||||||
\(914\) | 1.98399e12 | 0.0940331 | ||||||||
\(915\) | −1.00966e14 | −4.76189 | ||||||||
\(916\) | 2.20228e11 | 0.0103358 | ||||||||
\(917\) | 5.42910e12 | 0.253551 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.57192e13 | −1.18943 | −0.594713 | − | 0.803938i | \(-0.702734\pi\) | ||||
−0.594713 | + | 0.803938i | \(0.702734\pi\) | |||||||
\(920\) | 1.90160e13 | 0.875132 | ||||||||
\(921\) | −3.71169e13 | −1.69982 | ||||||||
\(922\) | −4.58470e12 | −0.208940 | ||||||||
\(923\) | −2.21124e13 | −1.00283 | ||||||||
\(924\) | 4.47068e11 | 0.0201767 | ||||||||
\(925\) | −5.36214e13 | −2.40824 | ||||||||
\(926\) | −2.19917e13 | −0.982899 | ||||||||
\(927\) | −1.90320e12 | −0.0846498 | ||||||||
\(928\) | 6.26840e12 | 0.277454 | ||||||||
\(929\) | −4.15886e12 | −0.183191 | −0.0915953 | − | 0.995796i | \(-0.529197\pi\) | ||||
−0.0915953 | + | 0.995796i | \(0.529197\pi\) | |||||||
\(930\) | 4.49496e13 | 1.97039 | ||||||||
\(931\) | −5.02176e12 | −0.219070 | ||||||||
\(932\) | −2.23066e12 | −0.0968414 | ||||||||
\(933\) | 3.54265e13 | 1.53060 | ||||||||
\(934\) | −4.20808e13 | −1.80935 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.21167e13 | −1.36770 | ||||||||
\(937\) | 9.33151e12 | 0.395479 | 0.197740 | − | 0.980255i | \(-0.436640\pi\) | ||||
0.197740 | + | 0.980255i | \(0.436640\pi\) | |||||||
\(938\) | 2.52293e12 | 0.106412 | ||||||||
\(939\) | −4.21279e13 | −1.76838 | ||||||||
\(940\) | 8.32104e12 | 0.347618 | ||||||||
\(941\) | −2.25028e13 | −0.935585 | −0.467792 | − | 0.883838i | \(-0.654950\pi\) | ||||
−0.467792 | + | 0.883838i | \(0.654950\pi\) | |||||||
\(942\) | −5.39752e13 | −2.23339 | ||||||||
\(943\) | 6.84083e12 | 0.281713 | ||||||||
\(944\) | 2.70481e13 | 1.10857 | ||||||||
\(945\) | −1.57073e12 | −0.0640706 | ||||||||
\(946\) | 1.55047e13 | 0.629438 | ||||||||
\(947\) | −7.23383e11 | −0.0292276 | −0.0146138 | − | 0.999893i | \(-0.504652\pi\) | ||||
−0.0146138 | + | 0.999893i | \(0.504652\pi\) | |||||||
\(948\) | 1.71225e12 | 0.0688540 | ||||||||
\(949\) | 7.24100e12 | 0.289802 | ||||||||
\(950\) | −1.49229e13 | −0.594426 | ||||||||
\(951\) | −4.64927e13 | −1.84320 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.77982e13 | 1.87713 | 0.938563 | − | 0.345107i | \(-0.112157\pi\) | ||||
0.938563 | + | 0.345107i | \(0.112157\pi\) | |||||||
\(954\) | −6.73039e12 | −0.263071 | ||||||||
\(955\) | 7.29830e13 | 2.83927 | ||||||||
\(956\) | 4.39999e12 | 0.170369 | ||||||||
\(957\) | −1.49796e13 | −0.577295 | ||||||||
\(958\) | −1.93300e13 | −0.741458 | ||||||||
\(959\) | 6.00710e12 | 0.229341 | ||||||||
\(960\) | −5.60402e13 | −2.12951 | ||||||||
\(961\) | −1.20876e13 | −0.457179 | ||||||||
\(962\) | −4.71326e13 | −1.77433 | ||||||||
\(963\) | −8.97327e12 | −0.336227 | ||||||||
\(964\) | 1.84973e12 | 0.0689862 | ||||||||
\(965\) | −2.68722e12 | −0.0997541 | ||||||||
\(966\) | −6.36764e12 | −0.235278 | ||||||||
\(967\) | −3.15015e13 | −1.15854 | −0.579272 | − | 0.815134i | \(-0.696663\pi\) | ||||
−0.579272 | + | 0.815134i | \(0.696663\pi\) | |||||||
\(968\) | −2.17712e13 | −0.796974 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.72771e13 | −0.626611 | ||||||||
\(971\) | 6.67606e12 | 0.241009 | 0.120505 | − | 0.992713i | \(-0.461549\pi\) | ||||
0.120505 | + | 0.992713i | \(0.461549\pi\) | |||||||
\(972\) | 4.80859e12 | 0.172790 | ||||||||
\(973\) | −6.96891e12 | −0.249263 | ||||||||
\(974\) | −4.85923e12 | −0.173002 | ||||||||
\(975\) | 1.45221e14 | 5.14646 | ||||||||
\(976\) | −5.94343e13 | −2.09659 | ||||||||
\(977\) | −4.15163e13 | −1.45778 | −0.728891 | − | 0.684630i | \(-0.759964\pi\) | ||||
−0.728891 | + | 0.684630i | \(0.759964\pi\) | |||||||
\(978\) | 3.29551e13 | 1.15186 | ||||||||
\(979\) | 5.27043e12 | 0.183368 | ||||||||
\(980\) | −5.97233e12 | −0.206836 | ||||||||
\(981\) | −1.14995e13 | −0.396430 | ||||||||
\(982\) | 3.36971e13 | 1.15635 | ||||||||
\(983\) | −9.03604e12 | −0.308665 | −0.154333 | − | 0.988019i | \(-0.549323\pi\) | ||||
−0.154333 | + | 0.988019i | \(0.549323\pi\) | |||||||
\(984\) | −2.05366e13 | −0.698313 | ||||||||
\(985\) | 3.78844e12 | 0.128232 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.93938e13 | 0.650482 | ||||||||
\(988\) | −1.46392e12 | −0.0488776 | ||||||||
\(989\) | −2.46461e13 | −0.819151 | ||||||||
\(990\) | −2.01069e13 | −0.665254 | ||||||||
\(991\) | 3.19314e13 | 1.05169 | 0.525844 | − | 0.850581i | \(-0.323749\pi\) | ||||
0.525844 | + | 0.850581i | \(0.323749\pi\) | |||||||
\(992\) | 5.61380e12 | 0.184058 | ||||||||
\(993\) | 5.23597e13 | 1.70894 | ||||||||
\(994\) | 6.29843e12 | 0.204641 | ||||||||
\(995\) | −3.19379e13 | −1.03300 | ||||||||
\(996\) | 5.13297e12 | 0.165273 | ||||||||
\(997\) | 3.11747e13 | 0.999248 | 0.499624 | − | 0.866242i | \(-0.333471\pi\) | ||||
0.499624 | + | 0.866242i | \(0.333471\pi\) | |||||||
\(998\) | −3.23445e13 | −1.03208 | ||||||||
\(999\) | −3.73326e12 | −0.118589 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 289.10.a.i.1.15 | 52 | ||
17.5 | odd | 16 | 17.10.d.a.8.10 | ✓ | 52 | ||
17.7 | odd | 16 | 17.10.d.a.15.10 | yes | 52 | ||
17.16 | even | 2 | inner | 289.10.a.i.1.16 | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.d.a.8.10 | ✓ | 52 | 17.5 | odd | 16 | ||
17.10.d.a.15.10 | yes | 52 | 17.7 | odd | 16 | ||
289.10.a.i.1.15 | 52 | 1.1 | even | 1 | trivial | ||
289.10.a.i.1.16 | 52 | 17.16 | even | 2 | inner |